On the reliability of polarization estimation using Rotation Measure Synthesis
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We benchmark the reliability of the rotation measure (RM) synthesis algorithm using the 1005 Centaurus A field sources of Feain et al. The RM synthesis solutions are compared with estimates of the polarization parameters using traditional methods. This analysis provides verification of the reliability of RM synthesis estimates. We show that estimates of the polarization parameters can be made at lower signal-to-noise ratio (S/N) if the range of RMs is bounded, but reliable estimates of individual sources with unusual RMs require unconstrained solutions and higher S/N. We derive from first principles the statistical properties of the polarization amplitude associated with RM synthesis in the presence of noise. The amplitude distribution depends explicitly on the amplitude of the underlying (intrinsic) polarization signal. Hence, it is necessary to model the underlying polarization signal distribution in order to estimate the reliability and errors in polarization parameter estimates. We introduce a Bayesian method to derive the distribution of intrinsic amplitudes based on the distribution of measured amplitudes. The theoretically derived distribution is compared with the empirical data to provide quantitative estimates of the probability that an RM synthesis solution is correct as a function of S/N. We provide quantitative estimates of the probability that any given RM synthesis solution is correct as a function of measured polarized amplitude and the intrinsic polarization amplitude compared to the noise.
Copyright © 2012 IOP Institute of Physics
This is an author-created, un-copyedited version of an article accepted for publication in The Astrophysical Journal. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at DOI: 10.1088/0004-637X/750/2/139.
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